Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 67, Issue 4, Pages 869-899Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-012-0572-3
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Funding
- RAPIDD program of the Science and Technology Directorate
- Department of Homeland Security
- Fogarty International Center, National Institutes of Health
- Center for Communicable Disease Dynamics
- Department of Epidemiology
- Harvard School of Public Health from the National Institute Of General Medical Sciences [U54GM088558]
- NIH [K01 AI091440]
- MRC [MR/K010174/1] Funding Source: UKRI
- Medical Research Council [G0600719B, MR/K010174/1B, MR/K010174/1] Funding Source: researchfish
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We consider the family of edge-based compartmental models for epidemic spread developed in Miller et al. (J R Soc Interface 9(70):890-906, 2012). These models allow for a range of complex behaviors, and in particular allow us to explicitly incorporate duration of a contact into our mathematical models. Our focus here is to identify conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the mass action model gives clear, rigorous conditions under which the mass action model is accurate.
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